Finding the exact delay bound for consensus of linear multi-agent systems

References

• Bernstein, D. (2005). Matrix mathematics. Princeton, NJ: Princeton University Press.
   Google Scholar
• Brewer, J. (1978). Kronecker products and matrix calculus in system theory. IEEE Transactions on Circuits and Systems, 25, 772–781.
   Google Scholar
• Cao, Y., Yu, W., Ren, W., & Chen, G. (2013). An overview of recent progress in the study of distributed multi-agent coordination. IEEE Transactions on Industrial Informatics, 9(1), 427–438.
   Web of Science ®Google Scholar
• Cepeda-Gomez, R., & Olgac, N. (2011a). An exact method for the stability analysis of linear consensus protocols with time delay. IEEE Transactions on Automatic Control, 56(7), 1734–1740.
   Web of Science ®Google Scholar
• Cepeda-Gomez, R., & Olgac, N. (2011b). Consensus analysis with large and multiple communication delays using spectral delay space concept. International Journal of Control, 84(12), 1996–2007.
   Web of Science ®Google Scholar
• Cepeda-Gomez, R., & Olgac, N. (2011c). Exhaustive stability analysis in a consensus system with time delay and irregular topologies. International Journal of Control, 84(4), 746–757.
   Web of Science ®Google Scholar
• Cepeda-Gomez, R., & Olgac, N. (2012). Stability analysis for the group dynamics consensus with time delay. European Journal of Control, 18(5), 456–468.
   Web of Science ®Google Scholar
• Cepeda-Gomez, R., & Olgac, N. (2013). Exact stability analysis of second-order leaderless and leader-follower consensus protocols with multiple time delays. Systems & Control Letters, 62(6), 482–495.
   Web of Science ®Google Scholar
• Cepeda-Gomez, R., & Olgac, N. (2014a). Consensus protocol under directed communications with two time delays. International Journal of Control, 87(2), 291–300.
   Web of Science ®Google Scholar
• Cepeda-Gomez, R., & Olgac, N. (2014b). Formation control based on a consensus protocol under directed communications with two time delays. International Journal of Systems Science. Advance online publication. doi:10.1080/00207721.2014.886745.
   Web of Science ®Google Scholar
• Ergenc, A.F., Olgac, N., & Fazelinia, H. (2007). Extended Kronecker summation for cluster treatment of LTI systems with multiple delays. SIAM Journal on Control and Optimization, 46(1), 143–155.
   Web of Science ®Google Scholar
• Fazelinia, H., Sipahi, R., & Olgac, N. (2007). Stability robustness analysis of multiple time-delayed systems using building block concept. IEEE Transactions on Automatic Control, 52(5), 799–810.
   Web of Science ®Google Scholar
• Godsil, C., & Royle, G. (2004). Algebraic graph theory. New York, NY: Springer.
   Google Scholar
• Kolmanovski, V.B., & Nosov, V.R. (1986). Stability of functional differential equations. London: Academic.
   Google Scholar
• Lin, P., & Jia, Y. (2009a). Consensus of second-order discrete multi-agent systems with nonuniform time delays and dynamically changing topologies. Automatica, 45(9), 2154–2158.
   Web of Science ®Google Scholar
• Lin, P., & Jia, Y. (2009b). Further results on decentralised coordination in networks of agents with second-order dynamics. IET Control Theory and Applications, 3(7), 957–970.
   Web of Science ®Google Scholar
• Lin, P., Jia, Y., Du, J., & Yuan, S. (2008). Distributed control of multi-agent systems with second-order agent dynamics and delay-dependent communications. Asian Journal of Control, 10(2), 254–259.
   Web of Science ®Google Scholar
• Lin, P., Jia, Y., & Li, L. (2008). Distributed robust H∞ consensus control in directed networks of agents with time-delay. Systems & Control Letters, 57(8), 643–653.
   Web of Science ®Google Scholar
• Liu, X., & Tian, Y.P. (2009). Formation control of multi-agent systems with heterogeneous communication delays. International Journal of Systems Science, 40(6), 627–636.
   Web of Science ®Google Scholar
• Meng, Z., Ren, W., Cao, Y., & Zheng, Y. (2011). Leaderless and leader-follower consensus with communications and input delays under a directed network topology. IEEE Transactions on Systems, Man and Cybernetics – Part B, 41(1), 75–88.
   PubMed Web of Science ®Google Scholar
• Münz, U., Papachristodoulou, A., & Allgower, F. (2010). Delay robustness in consensus problems. Automatica, 46(8), 1252–1265.
   Web of Science ®Google Scholar
• Olfati-Saber, R., & Murray, R. (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49(9), 1520–1533.
   Web of Science ®Google Scholar
• Olgac, N., & Holm-Hansen, B. (1994). A novel active vibration absorption technique: The delayed resonator. Journal of Sound and Vibration, 176(1), 93–104.
   Web of Science ®Google Scholar
• Olgac, N., & Sipahi, R. (2002). An exact method for the stability analysis of time-delayed linear time invariant systems. IEEE Transactions on Automatic Control, 47(5), 793–797.
   Web of Science ®Google Scholar
• Olgac, N., & Sipahi, R. (2005). Complete stability robustness of third order LTI multiple time delay systems. Automatica, 41(8), 1413–1422.
   Web of Science ®Google Scholar
• Olgac, N., & Sipahi, R. (2006). An improved procedure in detecting the stability robustness of systems with uncertain delay. IEEE Transactions on Automatic Control, 51(7), 1164–1165.
   Web of Science ®Google Scholar
• Peng, K., & Yang, Y. (2009). Leader-following consensus problems with a varying velocity leader and time-varying delays. Physica A: Statistical Mechanics and Its Applications, 388(2–3), 193–208.
   Web of Science ®Google Scholar
• Ren, W. (2008). On consensus algorithms for double integrator dynamics. IEEE Transactions on Automatic Control, 53(6), 1503–1509.
   Web of Science ®Google Scholar
• Ren, W., & Beard, R. (2005). Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control, 50(5), 655–661.
   Web of Science ®Google Scholar
• Schaefer, R.D. (1996). An introduction to nonassociative algebras. New York, NY: Dover.
   Google Scholar
• Sun, Y., & Wang, L. (2009a). Consensus of multi-agent systems in directed networks with nonuniform time-varying delay. IEEE Transactions on Automatic Control, 54(7), 1607–1613.
   Web of Science ®Google Scholar
• Sun, Y., & Wang, L. (2009b). Consensus problems in networks of agents with double integrator dynamics and time delays. International Journal of Control, 82(10), 1937–1945.
   Web of Science ®Google Scholar
• Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., & Shochet, O. (1995). Novel type of phase transition in a system of self-driven particles. Physical Review Letters, 75(6), 1226–1229.
   PubMed Web of Science ®Google Scholar
• Wang, Z., Zhang, W., & Guo, Y. (2010, September). Robust consensus output tracking of multi-agent systems with directed communications. In 3rd ASME Dynamics Systems and Control Conference (pp. 385–392). Cambridge, MA: ASME.
   Google Scholar
• Wang, Z., Zhang, W., & Guo, Y. (2011, June). Adaptive output consensus tracking of uncertain multi-agent systems. In American Control Conference (pp. 3387–3392). San Francisco, CA: IEEE.
   Google Scholar
• Wen, G., Peng, Z., Rahmani, A., & Yu, Y. (2014). Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics. International Journal of Systems Science, 45(9), 1892–1901.
   Web of Science ®Google Scholar
• Zhang, Y., & Tian, Y.P. (2014). Allowable delay bound for consensus of linear multiagent systems with communication delay. International Journal of Systems Science, 45(10), 2172–2181.
   Web of Science ®Google Scholar